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ITV SERIES MATH TALK: EXPLORING SCALE AND RATION - #114

GRADES 4 - 6

OVERVIEW

In this lesson students will explore the solar system, how to calculate the scale and ratio, and the uses to size and distance. Students will use scale and ratio to measure the actual size and distance of the solar system. Hands-on activities will engage students in learning.

LEARNING OBJECTIVES

• Students will be able to calculate the correct ratio using the same scale as was used to draw the solar system model.
• Students will be able to compare the scale sizes of planets to their actual sizes.
• Students will be able to understand the scale distances from the sun to the planets.
• Students will able to understand the scale size of the planets.
• Students will able to apply the scale of size and distance to hands-on activities.

PLANET CHARTS

• Planetary Data Distance Table
• Planetary Relative Size Table
• Make Models of the Planets Table
• Distances between Planets Table
• Bulletin Board Solar System
• Distances From the Sun
• Simple Scale Model of the Solar System
• Real and Scaled Sizes of the Sun and Planets
• Real and Scaled Distances of the Planets
• Scaled Model of Solar System
  using Tissue Toilet Paper

• Size of Plane

MATERIALS

• VCR
• 26 Math Learning Logs
• 26 Pencils and Stack of Paper for calculations
• Large Stack of Paper
• 26 Sets of Pictures of the Solar System
• 10 large white sheets of poster board
• 26 Coloring markers
• 10 to 12 Sets of Reference books for pictures of the planets
• Two or three roles of traditional school-grade toilet paper
• Marble, walnut, golf ball, acorn, basketball, soccer ball, softball, small grapefruit, kidney bean - enough for each student.
• 26 Metric rulers
• 26 Sets of Copies of the size and distance tables
• 26 Scissors
• 50 yards of Butcher paper
• 10 to 13 Measuring tapes or yardsticks
• Clay-different colors like blue, yellow, green, brown, orange, etc.
• Cardboard

PREVIEWING ACTIVITIES

Begin discussion with question such as the following:

• Why use these scale models in the classroom?
• Why use scale models with different scale factors?
• How can you use a scale table to determine the actual distance between two planets?
• These questions should get the discussion going in the correct direction about relationship between the scale and actual size of the solar system.

FOCUS FOR VIEWING

To give students a specific responsibility while viewing that the students are responsible for during and after the viewing to engage students' viewing attention.

Have students listen carefully as Maria Lopez in the video discussion what a scale represents. Hand out size and distance tables to students.

Also give students pictures of the planets in the solar system. Ask students to watch and write down what they learn about scale and ratio during the video.

VIEWING ACTIVITIES

BEGIN the video at the point just after Maria Lopez asks Buster why he wants to lose weight. STOP the Video after Maria explains to Buster what units of measure are. Ask the students what they think a unit of measure is? Make sure that they understand that every map or scale drawing contains a ratio, or scale. It is the ratio of a length in the map or scale drawing to an actual length. You can use a scale to find actual measures. The scale factor in the scale distance table of the solar system is 1 to 10 billion. As result, the Earth is 150 million km from the Sun. The scaled distance from the Sun is 15m.

RESUME the Video and play the section where the sailor goes to the Captain and tells him that their ship is only 10 centimeters from an iceberg. STOP the Video when the Captain explains the difference between a map and the real world. Discuss with the class what the difference the map is from the real world. What is the scale on a map or drawing used for? How do you calculate the distances between places?

RESUME the Video and play the section where the Captain states a map that measures New Jersey would have to be as big as the actual New Jersey. STOP the Video when the Captain says 10 centimeters equals 100 kilometers in the real world. Ask students if they now understand how the scale on a map works?

Explain to students that maps are drawn by cartographers, who use ratios, proportions, and scale to convert distances on the Earth to distances on paper. Further explain to students that a scale is used to determine distances on a map. For many maps, the scale compares inches or centimeters on a map to miles or kilometers on a real surface or space.

To compare distances on a map with actual distances, explain to the students that you use the ratio map distance divided by actual distance.

POST VIEWING ACTIVITIES

Discuss with the students the information learned in the video. Tell students, "We are going to look more closely at scale and ratio--in our journey through the Solar System."

Activity 1
Students will make a distance-scale solar system model with toilet paper. Students will identify attributes to classify planets in our solar system. In addition, ask students to draw and describe one planetary object. Students will observe the relative distance between planets. Explain to students that interplanetary travel is extremely difficult due to the almost unimaginable distances between the planets in our solar system. Voyager II, traveling at nearly 50,000 mph took 12 years to reach the planet Neptune.

Have student's record in their Math/Science Learning Logs how they would make a scale model of the distances between the planets using almost anything as a reference. Students will give their suggestions about the variety of ways to classify the planets of our solar system.

Discuss with the students that it is almost impossible to make a scale model of the solar system that is correct in both planetary diameter and distance. Using a 1m Sun and a 5mm Earth, Pluto would be almost one half mile away; using 1 sheet of toilet paper equals 10,000,000 miles.

Using the large poster paper, ask students to illustrate in detail the Sun and each of the nine planets on individual sheets (one object per sheet). Have students research and write facts about the object on the back of the poster. They will place all of the posters at the front of the room. Next, ask students to list as many ways as possible to classify (group) them by the appearance of the posters. Ask volunteers to roll out the school-grade toilet tissue, marking off the distances to the planets using a scale of one tissue = 10,000,000 miles (refer students to the scaled model of the solar system toilet paper table).

Have a student hold a planet-poster at each of the appropriate distances. Next, ask students, "In what ways can you classify the planets by their various attributes?" Ask Students how far is the Earth from the Sun? How far is the Earth from Mars? Compare the distances between neighboring planets. Which two are closest together? Which two are farthest apart? As a group, which set of planets is closest together--those nearest the Sun or farther out?

With other students, hypothesize about the effects of a planet's distance from the Sun. Which planets would be hottest? Which would be coldest? What would the Sun look like from each one? How long would a year be on each planet? Ask students to compare their ideas with each other.

Activity 2
How big are the planets? Bring a model of a ship or airplane to class and explain that it is built to scale. Tell students what the scale is. Inform students that when a model is built to scale, all of its parts are in correct proportion. That is, they are in the same proportion to one another as the parts of the "real or actual thing." Ask students to break up into groups of 2 or 3 each. Ask students to review reading the graduations on a metric ruler.

Draw an enlarged ruler on the chalkboard and show students which graduations represent millimeters. Explain to students that all data for the diameters of the planets have been rounded (size of planets table).

Students will each be given a copy of Sizes of Planets Table, which shows the length of each planet's diameter. The diameter is a line that goes from one side of a planet to the other side through its center. Additionally, the table also shows the sizes for scale models of the planets. Using this scale, 1 millimeter equals 1,000 kilometers.

Ask students to look at the pictures in this activity to help you choose the right color clay for your scale model. Students make the ball of clay with the right diameter for each planet. If your planet has rings, cut out the cardboard to make rings. Furthermore, you will need to make the hole in the cardboard a little smaller than your model so that the rings will stick to the scale model. Ask students to put the models in the order shown on the Size of Planets Table.

What planet is nearest the Sun? Explain to the students to compare the sizes of the planets, but not the distances between planets. The distances are much greater. How do the models made by other groups' compare with your group's model? Discuss with the students the sizes of the planets. Ask students which is the largest planet? Ask students which is the smallest planet? Is there any pattern in the sizes and order in which the planets are lined up? If so, what pattern do you see? Why are Venus and Earth called sisters?

POST VIEWING ACTIVITIES (CONT.)

Activity 3 (optional)
Modeling Planetary Sizes By relating the sizes of the different planets to familiar objects, this activity helps to reinforce the relative sizes of the planets. Bring to class the following familiar objects: enough for one each group - marble, walnut, golf ball, raisin, acorn, basketball, soccer ball, softball, grapefruit, kidney bean, and Post-It pads.

Ask students to label the objects from the Planetary Relative Size Table with Post-It pads as follows: Mercury--marble; Venus--walnut; Earth--golf ball; Moon--raisin; Mars--acorn; Jupiter--basketball; Saturn--soccer ball; Uranus--softball; Neptune--grapefruit; Pluto--bean.

Explain to the students that Uranus is slightly larger than Neptune is. If the grapefruit is larger than the softball, switch the labels.

Ask the students to arrange the planets in order of increasing size. Does it seem odd to you there are no medium sized planets? Ask the students are all the planets the same size? Is the Moon much smaller than all the planets? Is the Moon a planet? How big should the Sun be on this scale?

Explain to the students that the Sun would actually be over nine feet across--this is higher than an average classroom ceiling!

Scaled Model of Solar System using Tissue Toilet Paper

Why use the scale models involving size and distance of objects in the solar system?

• General Scientists use models everyday.
• Models can be conceptual, mathematical, and scale.
• Scale models are a concept with which students are already familiar in the context of model toys, maps, and globes.
• Scale models allow students to explore systems with scales from the microscopic to the astronomical that are beyond the realm of normal human experience.
• Mathematics Scale models utilize fractions, decimals, ratios, and proportions.
• Scale models allow students to make a connection between physical objects and mathematical concepts.
• Astronomy/Science Scale models of the solar system aid students in understanding the relative sizes and distances of objects in the solar system, an important foundation for studying other topics in astronomy.
• Scale models provide a concrete, hands-on, method of exploring the nature of our solar system in a classroom setting.
• Scale models of solar system objects compared with a model Earth (on the same scale) allow students to relate astronomical objects to the only planet with which they have direct experience.
• Scale Model Solar System matches the following Curriculum and Evaluation Standards for School Mathematics Science and math are intimately related, and it is difficult, it not impossible, to study the physical sciences without using math to some degree. This activity meets a wide variety of content standards in mathematics, and is as much a math activity as a science activity. This is especially true if students make their own calculations using the real sizes and/or distance of objects in the solar system and the provided scale factor to create their scale model solar systems.
• For the Scale Model Solar System activity, the primary mathematical themes are: problem solving, measurement, proportion, estimation, spatial relationships, representation of a real world situation with models (including the use of scale factor), using math in another subject (science) and critical thinking using mathematics.

EXTENSIONS

• Art--In A Wrinkle in Time, as Meg and her companions are traveling through space to find her father, they land briefly on a two-dimensional planet. Meg feels flattened like a paper doll. Have students draw what they think such a planet would look like.
• Health--Ask student to write reports describing the environmental conditions on Earth that allow us to live and the reasons why humans could not live on each of the other planets.
• Technology Connection--Videodisc--Access The Solar System to reinforce the concept that the nine planets have similarities and differences.
• Literature--Explain to the students that all but one of the planets were named for a Greek or Roman god or goddess. Invite students to identify those planets (Earth is the exception) and read about the mythological figure for which each planet was named. Students can make a chart of the names of the planets and brief descriptions of the corresponding mythological figures. Have the students display their charts. Challenge them to figure out why each planet was names as it was.
• Multicultural Connection--Have students research the accomplishments in space of the former Soviet Union. Students may find information in encyclopedias under the topics "space travel," "Cosmonauts," and "Soyuz spacecraft."
• Field Trip-- Visit the planetarium on the Washington State University campus.

Web Sites to Explore:

Solar System Trading Cards
http://amazing-space.stsci.edu/trading
-top-level.html

Introduction to the Nine Planets--
http://seds.lpl.arizona.edu/nineplanets
/nineplanets/intro.html

Solar System Exploration: The Planets
http://sse.jpl.nasa.gov/features/planets
/planetsfeat.html

For additional lesson plans and ideas relating to this topic and many others try TeacherSource at PBS Online! You will find activities, lesson plans, teacher guides and links to other great educational web sites! Search the database by keyword, grade level or subject area! Mathline and Scienceline are also great resources for teachers seeking teaching tips, lesson plans, assessment methods, professional development, and much more!

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